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• W3101920194 endingPage "2119" @default.
• W3101920194 startingPage "2085" @default.
• W3101920194 abstract "We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, P c (G), with very high accuracy. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent ν that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as R L and R H is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with ν = 2.37±0.02. Away from the transition it crosses over towards the Poisson distribution. We next investigate the plateau-to-insulator transition at strong magnetic fields. For a fully quantum coherent situation, we find a quantized Hall insulator with R H ≈h/e 2 up to R L ~20h/e 2 when interpreting the results in terms of most probable value of the distribution function P(R H ). Upon further increasing R L →∞, the Hall insulator with diverging Hall resistance [Formula: see text] is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure for the distributions P(R L ) and P(R H ). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law r -α . Similar to the classical percolation, we observe an enhancement of ν with decreasing α. These results exemplify the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization-delocalization transition." @default.
• W3101920194 created "2020-11-23" @default.
• W3101920194 creator A5054542530 @default.
• W3101920194 creator A5088921285 @default.
• W3101920194 date "2005-05-20" @default.
• W3101920194 modified "2023-10-18" @default.
• W3101920194 title "REAL-SPACE RENORMALIZATION-GROUP APPROACH TO THE INTEGER QUANTUM HALL EFFECT" @default.
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